Symbolic models

Figure3.70 Temperature response measured afteraheatcarrierfluid (oil,velocity0.35ms has been switchedfrom200tol 80°Catdifferentlocationsona micro heatexchangerplatelet. Measured values (symbols) model predictions (solid lines) [135],...

As the subject matter is often dif cult to visualize, symbols, models, and other graphic... 

Models are broadly distinguished on the one hand into material or physical or concrete, and on the other hand into abstract or conceptual or symbolic. Symbolic models include mathematical formulas and equations. Gilbert et al. (42) classified models according to their ontological status as follows mental, expressed, consensus, scientific, historical, and hybrid. Consensus, scientific, and historical models specifically developed for education are distinguished into teaching, curricular, and models of pedagogy. 

J.-C. Samin and P. Fisette Symbolic Modeling of Multibody Systems. 2003... 

Traditional symbolic models typically capture the semantic content of symbols through external devices, such as look-up tables and semantic networks. In this approach, symbols serve as pointers to semantic content, rather than capturing that content directly (see Hinton, 1990 Hummel Holy oak, 1997). 

Once the molecule is designed on a symbolic level, then the 3D structures of the conformational surface are directly constructed by using the 3D coordinate representations of the symbolic models, which are also coded in the template library. Cohen s procedure and related ones, however, are limited by the size and the nature of the sets of templates and assembly rules. The latter are not large enough to provide 3D building for complicated molecules such as bridged and polycyclic systems. For example, it is known that Cohen s script system often fails in generating 3D models of polycyclic molecules with more than three cycles. 

The symbol / models the fact that a resident can leave the nursing home or corresponds to the last resident assessment during the last 30 days before the data extraction. It is only used when we want to deduce the Markov model. Consequently, in the following example, the symbol / does not exist in Fig. 6. 

The second step concerns the identification of the words which corresponds to the translation of the initial sequence in order to take into account length of time spent in each cluster. Resident number 7 stayed in cluster number 3 from 06/24/2002 to 03/15/2004 (date at which the resident was evaluated and changed to cluster number 2). Thus resident number 7 stayed in cluster number 3 for about 22 periods of 30 days. The symbol modeling cluster number 3 for 30 days is c, consequently the initial sequence 33 becomes cccccccccccccccccccccc The resident stayed in cluster number 2 for 9 periods... 

Symbolic model checking 10 states and beyond. Information and Computationj 98(2) 142-170,1992. 

Using the symbolic model-checking facility supported by VIS, we have model-checked to prove that the arbitration algorithm ensures at-most one bus driver at any time. During this experiment, property-specific reductions achieved considerable reduction in model-checking time. 

In another experiment, symbolic model-checking of the Runway arbitration algorithm exposed a possible misunderstanding in a timely fashion. Some members of the Avalanche design team believed that two signals named Client-op and Effective-Client-op were implied to be almost the same , by the documentation. We model-checked an invariant Client-Op = Effect ive-Client-op which revealed that this assumption was incorrect, generating a useful error-trace. 

Statistics pertaining to our model-checking experiments are summarized in Table 1. This table shows that the complexity of these protocols in terms of the number of gates, latches, and reachable states is well within the reach of today s symbolic model-checking tools. Also, the property-specific model reduction heuristic used in VIS proved to be of great value in reducing the model-checking time. 

HW94] Cherly Harkness and Elizabeth Wolf. Verifying the summit bus converter protocols with symbolic model checking. Formal Methods in System Design, 4(2) 83-98, 1994. 

McM93] Kenneth L. McMillan. Symbolic Model Checking. Kluwer Academic Press, 1993. 

The FSM model is the one on which formal equivalence verification between two designs, and symbolic model checking are performed. It requires the previous flattening of hierarchical descriptions, and the elimination of all non-memorizing internal signals the initial structure is thus lost. 

Encrenaz, E. (1995) A Symbolic Relation for a Subset of VHDL 87 Descriptions and its Application to Symbolic Model Checking. Correct Hardware Design and Verification Methods 95, 328-342. 

Symbolic Model Checking for a Discrete Clocked Temporal Logic with Intervals... 

Symbolic Model Checking, Discrete Temporal Logic, CCTL, Extended Characteristic Functions, MTBDD... 

Symbolic model checking makes excessive use of Boolean functions. ROBDDs (R.E. Bryant 1986) are a compact and efficient representation of these functions. In contrast to ROBDDs, multi terminal binary decision diagrams (MTBDD) (E. Clarice et al. 1993,R.I. Baharetal. 1993) representpseuribBoo/ean ncrions. These functions map bit vectors to a finite set of elements. 

J.R. Burch, E.M. Clarke, K.L. McMillan, D.L. Dill L.J. Hwang (1990), Symbolic Model Checking 10 ° States and Beyond, in Proceedings of the Fifth Annual IEEE Symposium on Logic in Computer Science , IEEE Computer Society Press, Washington, D.C., pp. 1-33. 

S. V. Campos E. Clarke (1994), Real-Time Symbolic Model Checking for Dis-... 

T. Kropf J. Ruf (1997), Using MTBDDs for discrete timed symbolic model check-... 

J. R. Burch, E. M. Clarke, and D. E. Long. Symbolic Model Checking with Partitioned Transition Relations. In Proc. VLSP9L pages 49-58, Edimburgh, Scotland, August 1991. 

We present an inductive characterization for an invariant to stand in a given finite-state transition system. We show how this characterization can be computed by means of BDD-based operations, without performing a fixpoint iteration over sets of states as the CTL symbolic model checking algorithm does. 

A big step forward was made when McMillan (1993) proposed a new model checking algorithm for CTL, based on fixpoint computations of sets of states. In this algorithm, called symbolic model checking, binary decision diagrams (Bryant 1986) are used to represent both the transitions and the states of the model. Since sets of states are represented in intention by their characteristic functions, the size of the verified model is not bound by the memory of the computer carrying the verification and it is possible to verify systems that have several orders of magnitude more states. 

However, most of the systems designed today are much larger and, in order to achieve verification, symbolic model cheddng must be combined, often manually, with other techniques, such as abstraction and composition. It is... 

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